# Interdisciplinary Applied Mathematics

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a few microns.

The amplitude of the deviation from the isothermal condition is a function of the Knudsen and the Mach number. The deviation increases as the Knudsen or the Mach number increases.

At a fixed Knudsen number, changing the Mach number does not lead to any qualitative change in the temperature profile.

At a fixed Mach number the influence of the increase of the Knudsen number is to increase the depth of temperature minimum.

At a fixed Mach number, as the Knudsen number is increased, the (two symmetric) maxima in the temperature profile move near to the wall.

##### 5.5 Heat Transfer in Couette Microflows

In this section a two-dimensional channel extending from y = 0 to y = h is considered. The flow is driven by moving the top wall of the channel with a specified velocity U0. Thus, this case can be a prototype for a microrotor. Assuming a two-dimensional fully developed flow, the Navier-Stokes equations can be simplified to give linear velocity distribution in the channel. This can be written in nondimensional form

Jt = TT( П _ y/h + ^ Kn I 3 (7 — 1) Kn2 Re d% Uq ^    1 + 2-^£lL Kn 27Г    7 Ec dx

The corresponding volumetric flowrate per channel width is